This study investigates the effects of premixing oil with chemical dispersant at varying concentrations on the flow structure and droplet dynamics within a crude oil jet transitioning into a plume in a crossflow. It is motivated by the need to determine the fate of subsurface oil after a well blowout. The laboratory experiments consist of flow visualizations, in situ measurements of the time evolution of droplet-size distributions using holography, and particle image velocimetry to characterize dominant flow features. Increasing the dispersant concentration dramatically decreases the droplet sizes and increases their number, and accordingly, reduces the rise rates of droplets and the upper boundary of the plume. The flow within the plume consists primarily of a pair of counterrotating quasi-streamwise vortices (CVP) that characterize jets in crossflows. It also involves generation of vertical wake vortices that entrain small droplets under the plume. The evolution of plume boundaries is dominated by interactions of droplets with the CVP. The combined effects of vortex-induced velocity and significant quiescent rise velocity of large ($5 mm) droplets closely agree with the rise rate of the upper boundary of the crude oil plume. Conversely, the much lower rise velocity of the smaller droplets in oil-dispersant mixtures results in plume boundaries rising at rates that are very similar to those of the CVP center. The size of droplets trapped by the CVP is predicted correctly using a trapping function, which is based on a balance of forces on a droplet located within a horizontal eddy.